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At 2:22 of this video , the prof. Moungi bowendi motivates the ideal gas law by saying that

$$ \lim_{ p \to 0} p \overline{V} = f(T)$$

That is if we drop pressure and see how it changes the volume, keep multiplying the two quantities and find the limit, we would find that it always converges to some constant dependent of the temperature of the gas.

My question is, how exactly would we pull this of practically? Every time we change the pressure, we implicitly change the volume as well if the temperature is fixed. So, if all gas converges to the same the same constant at a given temperature, how would we do verify this because as we change the pressure the molar volume is also changing.

Second of all why did we take molar volume here? The lecture previously introduced the volume with overline as molar volume, was that an arbitrary choice or is there more importance in it?

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  • $\begingroup$ Do the BIPM thermometry guides answer the question "how exactly"? "Interpolating Constant-Volume Gas Thermometry": bipm.org/utils/common/pdf/ITS-90/… $\endgroup$
    – user137289
    Commented Sep 4, 2020 at 10:09
  • $\begingroup$ seems like it but the article is quite heavy to read $\endgroup$
    – Brian
    Commented Sep 4, 2020 at 13:36

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I do not like the way prof Moungi Bowendi introduces the ideal gas law. From his introduction it seems that the only requirement for the validity of perfect gas law is to have low pressure, independently on the temperature. This is clearly false, since every real gas shows departures from the perfect gas law, provided the temperature is low enough.

Anyway, the key point in his derivation is that at every temperature (I would add provided it is high enough) the product $p \overline{V}$ goes to a unique function $f(T)$ depending on temperature but independent on the substance the gas is made of. This is something which can be experimentally verified working with different substances.

There is nothing special in working with molar volume. It is just a conveninet way to take into account the fact that fixing $p$ and $T$ does not say anythong about the volume unless one specifies the amount of substance the sample is made of.

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  • $\begingroup$ Why is he wrong and what you're saying is right? Sure, experimental results is one thing but for what intuitive reason should we expect this to happen. I mean to ask, is there any model which describes the intuition of this? $\endgroup$
    – Brian
    Commented Sep 5, 2020 at 14:29
  • $\begingroup$ Secondly while we do all of this, what is happening to the volume? from my intuition, I think it should be very large $\endgroup$
    – Brian
    Commented Sep 5, 2020 at 14:29
  • $\begingroup$ @Buraian I wrote the reasin his presentation is misleading: he did not stressed that the validity of what he writes is depending on temperature too. The real reason is purely experimental (physics is not math!). However if you like to have a good theoretical argument, it is enough to take into account that within Statistical Mechanics, the ideal gas law can be obtained in the limit where Classical Mechanics is a good approximation of Quantum Mechanics and the kinetic energy is the dominant term in the Hamiltonian. Both conditions require high temperature. $\endgroup$
    – GiorgioP-DoomsdayClockIsAt-90
    Commented Sep 5, 2020 at 14:36
  • $\begingroup$ @Buraian About the volume as a function of pressure at fixed $T$, your intuition is correct. Low pressures imply large molar volumes. $\endgroup$
    – GiorgioP-DoomsdayClockIsAt-90
    Commented Sep 5, 2020 at 14:37

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